Advertisements
Advertisements
Question
In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.
Advertisements
Solution
In the given problem, we have the first and the nth term of an A.P. along with the sum of the n terms of A.P. Here, we need to find the number of terms and the common difference of the A.P.
Here,
The first term of the A.P (a) = 8
The nth term of the A.P (l) = 33
Sum of all the terms Sn = 123
Let the common difference of the A.P. be d.
So, let us first find the number of the terms (n) using the formula,
`123 = (n/2)( 8 + 33)`
`123 = (n/2) (41) `
`((123)(2))/41 = n`
`n = 246/41`
n = 6
Now, to find the common difference of the A.P. we use the following formula,
l = a + (n-1)d
We get,
33 = 8 + (6-1) d
33 = 8 + (5)d
`(33-8)/5 = d`
Further, solving for d,
`d =25/5`
d = 5
Therefore, the number of terms is n = 6 and the common difference of the A.P. d= 5 .
APPEARS IN
RELATED QUESTIONS
Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
If Sn1 denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).
In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant will be the same as the class, in which they are studying, e.g., a section of class I will plant 1 tree, a section of class II will plant 2 trees, and so on till class XII. There are three sections of each class. How many trees will be planted by the students?
Find the sum of all natural numbers between 1 and 100, which are divisible by 3.
Find the sum of the first 40 positive integers divisible by 3
Find the middle term of the AP 10, 7, 4, ……., (-62).
If 18, a, (b - 3) are in AP, then find the value of (2a – b)
Choose the correct alternative answer for the following question .
In an A.P. first two terms are –3, 4 then 21st term is ...
Find the sum (−5) + (−8)+ (−11) + ... + (−230) .
There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.
The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is
The common difference of an A.P., the sum of whose n terms is Sn, is
Q.3
Q.11
Q.14
In a Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find that:
(i) first term
(ii) common difference
(iii) sum of the first 20 terms.
If the numbers n - 2, 4n - 1 and 5n + 2 are in AP, then the value of n is ______.
If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021-22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year. |
Based on the above information answer the following questions.
- Find the production in the 1st year
- Find the production in the 12th year.
- Find the total production in first 10 years.
[OR]
In how many years will the total production reach 31200 cars?
Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60...... is 300?
Hence find the sum of all the terms of the Arithmetic Progression (A.P.)
